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posted by alyemi on .
A solution was diluted by a factor of 2 and then again using a 1 to 3 dilution. What is the dilution of concentrate in the final sample

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A solution was diluted by a factor of 2 and then again using a 1 to 3 dilution. What is the dilution of concentrate in the final sample or
If 15ul of a 4% solution is diluted up to 50ul, what is the concentration of the resulting solution? Include units with your answer 
Frankly, there is so much confusion about what 1 to 3 dilution means that I never use it. Approximately 50% believe 1:3 means add 1 part solute to 3 parts solvent while the other half thinks it means 1 part solute to a total of 3 parts.
So a factor of 2 means it was diluted to 1/2 of the original volume. Let's just say we had a concn of 10 mg/mL. Diluted by a factor of 2 means we have reduced the concn to 1/2 x 10 mg/mL = 5 mg/mL. Now if we add 1 part of the 5 mg/mL plus 3 parts solvent, we have 1/4 of 5 mg/mL = 1.25 mg/mL ASSUMING that the volumes are additive and they probably are at weak strengths. I know I will get a lot of feedback on this BUT I believe 1:3 SHOULD mean 1 to a total volume of 3. When we say dilute 1:10 almost everyone understands that to mean to take 1 mL (measured with a pipet) and add water to a total volume of 10 mL (with a volumetric flask). This way we don't worry about the volumes being additive or not. So a 5 mg/mL solution diluted 1:3 means we have 5 x 1/3 = ?? you figure it. So those are the two ways of doing it. Take your pick depending upon what you've been taught. 
For the other problem, it is not that ambiguous (except that we don't know if it is percent by volume or percent by mass).
4% x (15 uL/50 uL) = ??%